Average Error: 0.4 → 0.4
Time: 8.6s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 \cdot 1 - \left(v \cdot v\right) \cdot \left(v \cdot v\right)\right)} \cdot \left(1 + v \cdot v\right)\]
\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}
↓
\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 \cdot 1 - \left(v \cdot v\right) \cdot \left(v \cdot v\right)\right)} \cdot \left(1 + v \cdot v\right)
double f(double v, double t) {
        double r175159 = 1.0;
        double r175160 = 5.0;
        double r175161 = v;
        double r175162 = r175161 * r175161;
        double r175163 = r175160 * r175162;
        double r175164 = r175159 - r175163;
        double r175165 = atan2(1.0, 0.0);
        double r175166 = t;
        double r175167 = r175165 * r175166;
        double r175168 = 2.0;
        double r175169 = 3.0;
        double r175170 = r175169 * r175162;
        double r175171 = r175159 - r175170;
        double r175172 = r175168 * r175171;
        double r175173 = sqrt(r175172);
        double r175174 = r175167 * r175173;
        double r175175 = r175159 - r175162;
        double r175176 = r175174 * r175175;
        double r175177 = r175164 / r175176;
        return r175177;
}
↓
double f(double v, double t) {
        double r175178 = 1.0;
        double r175179 = 5.0;
        double r175180 = v;
        double r175181 = r175180 * r175180;
        double r175182 = r175179 * r175181;
        double r175183 = r175178 - r175182;
        double r175184 = atan2(1.0, 0.0);
        double r175185 = t;
        double r175186 = r175184 * r175185;
        double r175187 = 2.0;
        double r175188 = 3.0;
        double r175189 = r175188 * r175181;
        double r175190 = r175178 - r175189;
        double r175191 = r175187 * r175190;
        double r175192 = sqrt(r175191);
        double r175193 = r175186 * r175192;
        double r175194 = r175178 * r175178;
        double r175195 = r175181 * r175181;
        double r175196 = r175194 - r175195;
        double r175197 = r175193 * r175196;
        double r175198 = r175183 / r175197;
        double r175199 = r175178 + r175181;
        double r175200 = r175198 * r175199;
        return r175200;
}

Error

Bits error versus v

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.4

    \[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
  2. Using strategy rm

  3. Applied flip--0.4

    \[\leadsto \frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \color{blue}{\frac{1 \cdot 1 - \left(v \cdot v\right) \cdot \left(v \cdot v\right)}{1 + v \cdot v}}}\]

  4. Applied associate-*r/0.4

    \[\leadsto \frac{1 - 5 \cdot \left(v \cdot v\right)}{\color{blue}{\frac{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 \cdot 1 - \left(v \cdot v\right) \cdot \left(v \cdot v\right)\right)}{1 + v \cdot v}}}\]

  5. Applied associate-/r/0.4

    \[\leadsto \color{blue}{\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 \cdot 1 - \left(v \cdot v\right) \cdot \left(v \cdot v\right)\right)} \cdot \left(1 + v \cdot v\right)}\]

  6. Final simplification0.4

    \[\leadsto \frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 \cdot 1 - \left(v \cdot v\right) \cdot \left(v \cdot v\right)\right)} \cdot \left(1 + v \cdot v\right)\]

Reproduce

herbie shell --seed 2020062 
(FPCore (v t)
  :name "Falkner and Boettcher, Equation (20:1,3)"
  :precision binary64
  (/ (- 1 (* 5 (* v v))) (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (- 1 (* v v)))))